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Beam-Stack Search - Beam-Stack Search Integrating...

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Click to edit Master subtitle style 11/13/09 Beam-Stack Search: Integrating Backtracking with Beam Search Ring Zhou and Eric A. Hansen Presented by Paul Gross
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11/13/09 Beam-Stack Search Overview Complete, anytime algorithm O( dw ) Memory Complexity l d = depth of optimal solution, w = beam width Uses novel beam stack structure l Stores most promising, unexpanded nodes at each level l Bounds, admissibly prunes sub-optimal nodes Outperforms l Breadth-first Branch and Bound (BFBnB)
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11/13/09 Beam Search Algorithm Breadth-first approach l Bound level fringe size Size is beam width ( w ) Branches most w promising nodes at each level Width bound reduces complexity l Time, Memory: O(wd) w = 2 . . . Goal State
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11/13/09 Making Beam Search Complete Beam-Stack search l Builds off Breadth-first Beam Search Prune layers by beam width Each layer expands at most w nodes l Expand layers by f(n) bounds f(n) = g(n) + h(n) as in A*, where h(n) admissible l Beam Stack stores f(n) ranges for each layer Successor layer nodes have f(n) value in range l Backtracking pruned nodes by shifting f(n) ranges
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11/13/09 Beam-stack Search Algorithm Stack Level Open Closed Current Node Beam Width ( w ) Upper f(n) Bound S Current Level Best Goal A B C 2 2 3 4 6 5 2 6 2 4 D E F G H I J 1 0 1 1 2 2 0 2 2 2 g(n) = V h(n) = V 3
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11/13/09 Beam-stack Search Algorithm Stack [ 0 , 10 ) Level Open Closed Current Node Beam Width ( w ) 2 Upper f(n) Bound 10 S Current Level Best Goal g(n) = V h(n) = V
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11/13/09 Beam-stack Search Algorithm Stack 0 10 Level Open Closed 0 S Current Node S Beam Width ( w ) 2 Upper f(n) Bound 10 S Current Level 0 Best Goal g(n) = V h(n) = V
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11/13/09 Beam-stack Search Algorithm Stack 0 10 Level Open Closed 0 S 1 Current Node S Beam Width ( w ) 2 Upper f(n) Bound 10 S Current Level 0 Best Goal g(n) = V h(n) = V
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11/13/09 Beam-stack Search Algorithm Stack 0 10 Level Open Closed 0 S 1 Current Node S Beam Width ( w ) 2 Upper f(n) Bound 10 S Current Level 0 Best Goal A 2 1 g(n) = V h(n) = V f(A) = g(A) + h(A) = 2 + 1 = 3
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11/13/09 Beam-stack Search Algorithm Stack 0 10 Level Open Closed 0 S 1 A Current Node S Beam Width ( w ) 2 Upper f(n) Bound 10 S Current Level 0 Best Goal A 2 1 g(n) = V h(n) = V f(A) = g(A) + h(A) = 2 + 1 = 3
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11/13/09 Beam-stack Search Algorithm Stack 0 10 Level Open Closed 0 S
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